# The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is : Option 1) $8\Omega$ Option 2) $16\Omega$ Option 3) $1\Omega$ Option 4) $6\Omega$

Heat developed in a resistor -

When a steady current flows through a resistance R for time t , the loss in electric potential energy appears as increased thermal energy(Heat H) of resistor and $H=i^2Rt$

The power devoleped = $\frac{energy}{time}=i^2R=iR=\frac{V^2}{R}$      (from Ohm's law)

- wherein

Unit of heat is joule (J)

Unit of power is watt (W)

$P=\frac{v^{2}}{Req}$

$\Rightarrow Req=\frac{v^{2}}{P}=\frac{16^{2}}{4}=64\Omega$

$\Rightarrow 64=2R+R+4R+R$

$\Rightarrow 64=8R$

$\Rightarrow 8=R$

$\Rightarrow R=8\Omega$

Option 1)

$8\Omega$

Option 2)

$16\Omega$

Option 3)

$1\Omega$

Option 4)

$6\Omega$

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